According to the webpage titled "Materials for the History of Statistics" by the Department of Mathematics at the University of York, a major text on this subject is:
Oscar Sheynin, Theory of Probability: A Historical Essay (published by NG Verlag 2005, ISBN 3-938417-15-3)
The book is packed full of names, dates, ideas, and references. It's probably a good contender for what you're looking for.
In the Preface to the book, the author tells us that:
The book is intended for those interested in the history of
mathematics or statistics and more or less acquainted with the latter.
It will also be useful for statisticians.
He then goes on to give a short outline of the book:
I describe the origin of the notions of randomness and subjective or
logical probability in antiquity, discuss how laymen comprehended the
main notions of the theory of probability, dwell on the birth of
political arithmetic and study the history of the theory proper. I
also trace the development of statistics and its penetration into
natural sciences as well as the history of the mathematical treatment
of observations (Ptolemy, Al-Biruni, Kepler, the classical error
theory). I stop at the axiomatization of probability and at the birth
of the real mathematical statistics, i.e., at Kolmogorov and Fisher.
The author appears to be active at making revisions to the book, so it would be worth visiting his website to see the latest available version of the book and his other related publications.